10 Prof. J. R. Young on the General Expression 



it is no wonder that they should be so, when we consider how 

 vastly greater must be the force required to uplift the' rocky 

 crust of the earth and wrench it asunder, than that which will 

 support a column of water equal to the thickness of that 

 crust. 



Since the foregoing paper was read, I have rather hastily 

 examined some other portions of water taken from different 

 pseudomorphous crystals. One of those portions contained 

 muriatic and sulphuric acids, iron, a trace of lime, and of 

 common salt. Acid was a little in excess, and some peroxide 

 of iron was left in the cavity from which the water was taken. 

 In another the same acids were detected and some iron. In 

 the third portion there seemed to be nothing besides a little 

 common salt. In many of the octahedral cavities, oxide of 

 iron was found, and sometimes iron pyrites or copper pyrites 

 adhering to the sides; these were apparently deposited from 

 some of the water which had entered the crystals in some in- 

 stances, but in others they were evidently imbedded in the 

 fluor, and, adhering to the deposit of quartz, were not dissolved 

 with the former. 



Earthy carbonate of iron occurs in some cavities mixed with 

 very minute crystals of quartz; and I have one pseudomor- 

 phous quartz crystal which is filled with fragments of fluor, 

 intermixed with translucent fragments of carbonate of iron 

 and earthy carbonate of iron, all curiously cemented together 

 into one mass ; the iron ore being rather in excess. 



I have also some hollow pseudomorphous crystals of quartz 

 formed originally on carbonate of iron, which appear to be 

 water-tight, and yet the latter substance has, like the fluor, 

 been abstracted. 



III. On the General Expression for the Sum of an Lifinite 

 Geometrical Series. By J. 11. Young, Professor of Mathe- 

 matics in Belfast College*. 



^I^HE general expression for the sum 



4 1— x + x* — x z + x A — &c. 



is 



1 x c 



of the infinite series 



S = 



l+x t+jr 



which reduces to — — when # is a proper fraction, either po- 

 * Communicated by the Author. 



